The effect of curved boundaries on the distribution of electrical stress round conductors

The paper investigates by the method of conformal transformation the distribution of electrical stress round certain systems of conductors which are important in high-tension practice. In particular the effect of rounding the edges of the conductors in reducing the high stresses at the edges is found quantitatively. The methods used are applied to calculate the variation of breakdown voltage with spacing distance between the electrodes. The two-thirds power law is derived as a limiting case for some of the electrodes, and the effect of variation of electrode shape and of physical assumptions is shown. The theoretical results are compared with such experimental data as are available. Approximate formulae are derived for the capacity of coaxial rectangular cylinders, which are an extension of the well-known correction for the corner of a Leyden jar, and their application to heat conduction problems is pointed out. The results are reduced to graphical form.